Unfortunately, no one can be told what the Matrix is. You have to see it for yourself.
For an object function $f(x,y)$, the Radon transform $Rf(x,y)=p(\theta,t)$ is the line integral over $f$ on all points parameterised by the line $L(\theta, t) = x\cos{\theta} + y\sin{\theta} = t, \forall \theta \in [0, 2\pi)$. Define a predictor function $p_{\theta}(t)$ as the Radon Transform evaluated at a single angle $\theta$ (i.e. a single projection of the object function onto a line).
The Fourier Slice Theorem states that the Fourier transform of the predictor function, $P_{\theta}(\omega)$, is equal to the Fourier Transform of the object function evaluated along a line through the origin at an angle corresponding to the predictor, $F(\omega\cos{\theta}, \omega\sin{\theta})$.
This theorem is useful in MRI image reconstruction where all radio signals from a slice, during the post-excitation precession, are projected onto a line at the receiver.
The Fourier Transform of the object function is, by definition: $$F(k_x, k_y) = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f(x,y)e^{-j2\pi(k_xx+k_yy)}dxdy$$
The Fourier Transform of the predictor function is, by definition: $$P_{\theta}(\omega) = \int_{-\infty}^{\infty}p_{\theta}(t)e^{-j2\pi\omega t}dt$$
Using the Radon Transform, the predictor can be defined in terms of the object function: $$p_{\theta}(t) = \mathbb{R}f(\theta,t) = \int_{L(\theta,t)}f(x,y)ds$$
Where the line integral is over: $$L(\theta,t) = {(x,y) \in \mathbb{R} \times \mathbb{R}\colon x\cos{\theta} + y\sin{\theta}} = t$$
Substituting this representation into the Fourier Transform of the predictor function gives: $$P_{\theta}(\omega) = \int_{-\infty}^{\infty} \int_{L(\theta,t)}f(x,y)ds \cdot e^{-j2\pi\omega t}dt$$
This can be factored into a double integral by expressing the line integral in the $(x,y)$ space: $$P_{\theta}(\omega) = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} f(x,y)e^{-j2\pi\omega(x\cos{\theta} + y\sin{\theta})}dxdy$$
Comparison with the Fourier Transform of the object function gives: $$P_{\theta}(\omega) = F(\omega\cos{\theta}, \omega\sin{\theta})$$
using Images, Plots, ImageView, FFTW
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It will be removed in a future version (julia:2484): Gtk-WARNING **: 10:57:12.634: Theme parsing error: gtk-widgets.css:41:33: The style property GtkWidget:separator-height is deprecated and shouldn't be used anymore. It will be removed in a future version (julia:2484): Gtk-WARNING **: 10:57:12.634: Theme parsing error: gtk-widgets.css:42:32: The style property GtkWidget:wide-separators is deprecated and shouldn't be used anymore. It will be removed in a future version (julia:2484): Gtk-WARNING **: 10:57:12.634: Theme parsing error: gtk-widgets.css:43:27: The style property GtkWidget:link-color is deprecated and shouldn't be used anymore. It will be removed in a future version (julia:2484): Gtk-WARNING **: 10:57:12.634: Theme parsing error: gtk-widgets.css:44:35: The style property GtkWidget:visited-link-color is deprecated and shouldn't be used anymore. It will be removed in a future version (julia:2484): Gtk-WARNING **: 10:57:12.634: Theme parsing error: gtk-widgets.css:126:19: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:134:19: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:141:24: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:142:24: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:169:26: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:184:27: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:258:44: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:259:39: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:391:27: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:402:30: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:442:23: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:446:18: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:458:18: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.635: Theme parsing error: gtk-widgets.css:528:38: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:684:32: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:685:24: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:696:10: not a number (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:696:24: Using Pango syntax for the font: style property is deprecated; please use CSS syntax (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:739:37: The style property GtkMenuItem:horizontal-padding is deprecated and shouldn't be used anymore. It will be removed in a future version (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:786:38: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:787:40: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:788:48: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:789:50: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:790:44: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:791:46: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:792:52: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:793:54: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:794:47: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:795:49: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:796:21: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:797:23: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:802:36: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:803:38: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:804:39: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:805:41: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:829:34: The :inconsistent pseudo-class is deprecated. Use :indeterminate instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:866:34: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:986:33: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.636: Theme parsing error: gtk-widgets.css:1008:33: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1025:33: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1031:35: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1041:28: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1148:35: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1313:32: The style property GtkWidget:wide-separators is deprecated and shouldn't be used anymore. It will be removed in a future version (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1325:30: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1326:29: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1333:37: The style property GtkMenuItem:horizontal-padding is deprecated and shouldn't be used anymore. It will be removed in a future version (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1396:30: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1402:30: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1405:30: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1429:30: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.637: Theme parsing error: gtk-widgets.css:1430:30: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.638: Theme parsing error: gtk-widgets.css:1463:27: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.638: Theme parsing error: gtk-widgets.css:1505:18: The 'outline-radius' property has been renamed to '-gtk-outline-radius' (julia:2484): Gtk-WARNING **: 10:57:12.638: Theme parsing error: gtk-widgets.css:1510:28: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1578:14: not a number (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1578:14: Expected a string. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1607:15: The 'icon-shadow' property has been renamed to '-gtk-icon-shadow' (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1616:15: The 'icon-shadow' property has been renamed to '-gtk-icon-shadow' (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1630:15: The 'icon-shadow' property has been renamed to '-gtk-icon-shadow' (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1640:15: The 'icon-shadow' property has been renamed to '-gtk-icon-shadow' (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1699:29: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1700:24: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1719:32: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1720:27: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1731:39: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1732:40: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1733:34: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1734:35: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1774:44: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1775:36: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1776:39: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1777:31: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1781:36: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.639: Theme parsing error: gtk-widgets.css:1782:31: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.640: Theme parsing error: gtk-widgets.css:1788:41: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.640: Theme parsing error: gtk-widgets.css:1792:44: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.640: Theme parsing error: gtk-widgets.css:1793:39: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.640: Theme parsing error: gtk-widgets.css:1801:39: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.640: Theme parsing error: gtk-widgets.css:1804:34: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.641: Theme parsing error: gtk-widgets.css:1833:15: The 'icon-shadow' property has been renamed to '-gtk-icon-shadow' (julia:2484): Gtk-WARNING **: 10:57:12.641: Theme parsing error: gtk-widgets.css:1841:43: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.642: Theme parsing error: gtk-widgets.css:1843:52: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.642: Theme parsing error: gtk-widgets.css:1848:57: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.642: Theme parsing error: gtk-widgets.css:1850:66: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.642: Theme parsing error: gtk-widgets.css:1862:43: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.642: Theme parsing error: gtk-widgets.css:1864:52: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.642: Theme parsing error: gtk-widgets.css:1869:69: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.643: Theme parsing error: gtk-widgets.css:1871:78: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.643: Theme parsing error: gtk-widgets.css:1885:43: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.643: Theme parsing error: gtk-widgets.css:1887:52: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.643: Theme parsing error: gtk-widgets.css:1892:68: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.643: Theme parsing error: gtk-widgets.css:1894:77: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.643: Theme parsing error: gtk-widgets.css:1908:43: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.643: Theme parsing error: gtk-widgets.css:1910:52: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.643: Theme parsing error: gtk-widgets.css:1915:68: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.643: Theme parsing error: gtk-widgets.css:1917:77: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.644: Theme parsing error: gtk-widgets.css:2004:30: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.644: Theme parsing error: gtk-widgets.css:2028:30: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.644: Theme parsing error: gtk-widgets.css:2029:32: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.644: Theme parsing error: gtk-widgets.css:2080:15: The 'icon-shadow' property has been renamed to '-gtk-icon-shadow' (julia:2484): Gtk-WARNING **: 10:57:12.644: Theme parsing error: gtk-widgets.css:2086:15: The 'icon-shadow' property has been renamed to '-gtk-icon-shadow' (julia:2484): Gtk-WARNING **: 10:57:12.644: Theme parsing error: gtk-widgets.css:2118:13: The :insensitive pseudo-class is deprecated. Use :disabled instead. (julia:2484): Gtk-WARNING **: 10:57:12.644: Theme parsing error: gtk-widgets.css:2121:21: The '-gtk-image-effect' property has been renamed to '-gtk-icon-effect' (julia:2484): Gtk-WARNING **: 10:57:12.644: Theme parsing error: gtk-widgets.css:2125:18: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.644: Theme parsing error: gtk-widgets.css:2132:18: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.645: Theme parsing error: unity.css:109:15: The 'icon-shadow' property has been renamed to '-gtk-icon-shadow' (julia:2484): Gtk-WARNING **: 10:57:12.646: Theme parsing error: gedit.css:65:67: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.646: Theme parsing error: gedit.css:102:15: The 'icon-shadow' property has been renamed to '-gtk-icon-shadow' (julia:2484): Gtk-WARNING **: 10:57:12.646: Theme parsing error: gedit.css:148:42: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.646: Theme parsing error: gedit.css:152:68: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.646: Theme parsing error: gedit.css:156:51: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.646: Theme parsing error: gedit.css:163:77: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.647: Theme parsing error: nautilus.css:29:47: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.647: Theme parsing error: nautilus.css:40:16: The 'outline-radius' property has been renamed to '-gtk-outline-radius' (julia:2484): Gtk-WARNING **: 10:57:12.647: Theme parsing error: nautilus.css:50:71: Using one color stop with linear-gradient() is deprecated. (julia:2484): Gtk-WARNING **: 10:57:12.647: Theme parsing error: nautilus.css:51:71: Using one color stop with linear-gradient() is deprecated. (julia:2484): Gtk-WARNING **: 10:57:12.648: Theme parsing error: gnome-panel.css:71:35: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.648: Theme parsing error: gnome-panel.css:72:35: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.648: Theme parsing error: gnome-panel.css:82:28: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.648: Theme parsing error: gnome-panel.css:83:28: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.648: Theme parsing error: gnome-panel.css:98:36: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.648: Theme parsing error: gnome-panel.css:104:36: The :prelight pseudo-class is deprecated. Use :hover instead. (julia:2484): Gtk-WARNING **: 10:57:12.649: Theme parsing error: unity-greeter.css:49:30: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.649: Theme parsing error: unity-greeter.css:53:29: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.649: Theme parsing error: unity-greeter.css:58:23: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.649: Theme parsing error: unity-greeter.css:59:22: The :focused pseudo-class is deprecated. Use :focus instead. (julia:2484): Gtk-WARNING **: 10:57:12.649: Theme parsing error: calendar.css:9:18: The 'outline-radius' property has been renamed to '-gtk-outline-radius' Gtk-Message: 10:57:12.656: Failed to load module "canberra-gtk-module" Gtk-Message: 10:57:12.657: Failed to load module "canberra-gtk-module"
# Load brain MRI
mri = load("mri_small.png")
mri = convert(Array{Float64}, Gray.(mri))
mri_view = heatmap(reverse(abs.(mri),dims=1), c=:viridis)
# Plot the fourier transform, again, on a log scale for visibility
mri_fft = fftshift(fft(mri))
fft_view = heatmap(reverse(log.(abs.(mri_fft).+1.1),dims=1), c=:viridis)
plot(mri_view, fft_view, layout = (1, 2), legend = false, size=(1000, 400))
kspace = zeros(Complex{Float64}, size(mri_fft))
reconstruction = zeros(Float64, size(mri_fft))
cartesian_animation = @animate for i in 1:size(kspace,2)
kspace[:,i] = mri_fft[:,i]
reconstruction = ifft(ifftshift(kspace))
kspace_view = heatmap(reverse(log.(abs.(kspace).+1.1),dims=1), c=:viridis)
reconstruction_view = heatmap(reverse(abs.(reconstruction),dims=1), c=:viridis)
plot(kspace_view, reconstruction_view, layout = (1, 2), legend = false, size=(1000, 400))
end every 5
gif(cartesian_animation, "cartesian_animation.gif", fps = 5)
┌ Info: Saved animation to │ fn = /home/sam/Documents/UniversityWork/CompressiveSensingForMagneticResonanceImaging/notebooks/exercise2/cartesian_animation.gif └ @ Plots /home/sam/.julia/packages/Plots/8GUYs/src/animation.jl:102